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A graph discretization of the Laplace–Beltrami operator

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 06 Jan 2015Embargo end date: 01 Jan 2013 United Kingdom Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Journal of Spectral Theory, volume 4, pages 675-714 (issn: 1664-039X, eissn: 1664-0403,

Authors: Burago, D; Ivanov, S; Kurylev, Y;

doi: 10.4171/jst/83 , 10.48550/arxiv.1301.2222

arXiv: http://arxiv.org/abs/1301.2222

A graph discretization of the Laplace–Beltrami operator

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Abstract

We show that eigenvalues and eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

Country

United Kingdom

Related Organizations

Pennsylvania State University
United States
Steklov Mathematical Institute
Russian Federation
Department of Mathematical Sciences
Russian Federation
University College London
United Kingdom
Russian Academy of Sciences
Russian Federation

Keywords

Mathematics - Differential Geometry, RIEMANNIAN-MANIFOLDS, Riemannian, Laplace, graph, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), CONVERGENCE, 58J50, 58J60, 65N25, 53C21, 05C50, FOS: Mathematics, discretization, Spectral Theory (math.SP), Analysis of PDEs (math.AP)

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